Sample Chaos Theory Research Paper. Browse other research paper examples and check the list of research paper topics for more inspiration. iResearchNet offers academic assignment help for students all over the world: writing from scratch, editing, proofreading, problem solving, from essays to dissertations, from humanities to STEM. We offer full confidentiality, safe payment, originality, and money-back guarantee. Secure your academic success with our risk-free services. Chaos theory is the study of deterministic difference (differential) equations that display sensitive dependence upon initial conditions (SDIC) in such a way as to generate time paths that look random. This research paper (a) explains what ‘chaos’ is in mathematics, (b) explains why economists became interested in this concept, (c) sketches economic forces that can ‘smooth’ out dynamical irregularities that can lead to chaos, (d) very briefly discusses theoretical models that generate chaotic dynamical systems as equilibria, and (e) discusses empirical testing for chaos. We shall spend most of the time on (e) because even though the vast bulk of studies has not found convincing evidence for chaotic dynamics that are short term predictable (out-of-sample) using nonlinear methods with high ability to detect chaos, the quest for chaos has generated useful statistical methods. 1. Chaos The mathematical apparatus for rigorous treatment of chaos can be quite intimidating to the nonmathematician. Therefore we shall attempt to explain the concepts verbally as much as possible. This expositional strategy will allow the reader to decide whether it is worth their while to investigate this area further. Reference to wide-ranging surveys are given. We follow Brock (1986) for a very brief treatment of some mathematics of chaos below. A deterministic discrete time dynamical system on n-dimensional space is a system, of n difference equations in n variables. Here F is a map from n-dimensional real space to itself, x (t ) and x (t +1) are n-dimensional vectors at date t and t +1 respectively, x0 denotes the initial condition vector, and t is time. A useful pedagogical example is the scalar ‘tent map’ T from the closed interval to itself defined by The hallmark of chaos is SDIC, i.e. for two nearby initial conditions, x (0), y (0), the map F magnifies the distance between them: for most pairs of nearby initial conditions. Here denotes a distance measure. The tent map (2) illustrates this idea nicely because |x (0) -y (0)| is magnified by a factor of two for small enough |x (0) – y (0)| except for the rare case where x (0), y (0) straddle the maximizer, x = 0.5. A popular way to precisely capture the idea of SDIC and to measure it is the largest Lyapunov exponent, L, which is defined by the following limit as h tends to infinity, Here DG denotes the n by n derivative matrix of map G, Fh (x (0)) denotes the application of map F to the n-vector x (0) h times, v denotes a nonzero n-dimensional direction vector, ‘ e denotes dot product, |·| denotes The post Chaos Theory Research Paper appeared first on iResearchNet .